pdf. (version 6.0 uploaded Tue 28/5/13)
Abstract |
The animation below summarises the message of this technical
report. On the left, the data from three farms (born in 87, 91, and
93) are shown in yellow, magenta, and grey; they are the sum of
a age-dependent
performance function f(a) [top left] and a wind variable v_t [middle left].
(The site 'fixed effects 'variables u1, u2, u3 are all actually
identical in this
cartoon example.)
On the right, the identical data can be produced by adding the orange
curve f(a) to the site-dependent 'fixed effects' variables
u1, u2, u3 (shown in green), thus obtaining the orange curves shown bottom
right, then adding the wind variable [middle right] shown in blue (v_t).
This model (which I call "the underlying model" in the paper)
has an unconstrained degree of freedom.
The underlying model can, for example, fit the data
with a steeply
dropping age-performance function (f),
a steeply rising trend in national wind conditions (v),
and a steep downward trend in the effectiveness of wind
farms as a function of their
commissioning date (u1, u2, u3); this parameter-fit fits the data exactly
as well as the true parameter setting.
The model actually used by Hughes differs in a a few detailed ways
from the "underlying model"; in particular, some time-dependent variables
are represented with month resolution, and some with year resolution.
The statements that I have made apply to the underlying model,
and only approximately to the actual Hughes model.
Nevertheless, I am confident that the flaw I have identified in the
underlying model is the essential explanation of the spurious
results from Hughes's analysis.